148 research outputs found
Self-adjoint extensions and SUSY breaking in Supersymmetric Quantum Mechanics
We consider the self-adjoint extensions (SAE) of the symmetric supercharges
and Hamiltonian for a model of SUSY Quantum Mechanics in with a
singular superpotential. We show that only for two particular SAE, whose
domains are scale invariant, the algebra of N=2 SUSY is realized, one with
manifest SUSY and the other with spontaneously broken SUSY. Otherwise, only the
N=1 SUSY algebra is obtained, with spontaneously broken SUSY and non degenerate
energy spectrum.Comment: LaTeX. 23 pages and 1 figure (minor changes). Version to appear in
the Journal of Physics A: Mat. and Ge
A calculation with a bi-orthogonal wavelet transformation
We explore the use of bi-orthogonal basis for continuous wavelet
transformations, thus relaxing the so-called admissibility condition on the
analyzing wavelet. As an application, we determine the eigenvalues and
corresponding radial eigenfunctions of the Hamiltonian of relativistic
Hydrogen-like atoms.Comment: 18 pages, see instead physics/970300
Massless fermions in a bag at finite density and temperature
We introduce the chemical potential in a system of massless fermions in a bag
by impossing boundary conditions in the Euclidean time direction. We express
the fermionic mean number in terms of a functional trace involving the Green's
function of the boundary value problem, which we study analytically. Numerical
evaluations are made, and an application to a simple hadron model is discussed.Comment: 14 pages, 3 figures, RevTe
Aharonov-Bohm effect in a Class of Noncommutative Theories
The Aharonov-Bohm effect including spin-noncommutative effects is considered.
At linear order in , the magnetic field is gauge invariant although
spatially strongly anisotropic. Despite this anisotropy, the
Schr\"odinger-Pauli equation is separable through successive unitary
transformations and the exact solution is found. The scattering amplitude is
calculated and compared with the usual case. In the noncommutative
Aharonov-Bohm case the differential cross section is independent of .Comment: 10 page
Determinants of Dirac operators with local boundary conditions
We study functional determinants for Dirac operators on manifolds with
boundary. We give, for local boundary conditions, an explicit formula relating
these determinants to the corresponding Green functions. We finally apply this
result to the case of a bidimensional disk under bag-like conditions.Comment: standard LaTeX, 24 pages. To appear in Jour. Math. Phy
Noncommutativity in (2+1)-dimensions and the Lorentz group
In this article we considered models of particles living in a
three-dimensional space-time with a nonstandard noncommutativity induced by
shifting canonical coordinates and momenta with generators of a unitary
irreducible representation of the Lorentz group. The Hilbert space gets the
structure of a direct product with the representation space, where we are able
to construct operators which realize the algebra of Lorentz transformations. We
study the modified Landau problem for both Schr\"odinger and Dirac particles,
whose Hamiltonians are obtained through a kind of non-Abelian Bopp's shift of
the dynamical variables from the ones of the usual problem in the normal space.
The spectrum of these models are considered in perturbation theory, both for
small and large noncommutativity parameters. We find no constraint between the
parameters referring to no-commutativity in coordinates and momenta but they
rather play similar roles. Since the representation space of the unitary
irreducible representations SL(2,R) can be realized in terms of spaces of
square-integrable functions, we conclude that these models are equivalent to
quantum mechanical models of particles living in a space with an additional
compact dimension.Comment: PACS: 03.65.-w; 11.30.Cp; 02.40.Gh, 19 pages, no figures. Version to
appear in Physical Review
QED vacuum fluctuations and induced electric dipole moment of the neutron
Quantum fluctuations in the QED vacuum generate non-linear effects, such as
peculiar induced electromagnetic fields. In particular, we show here that an
electrically neutral particle, possessing a magnetic dipole moment, develops an
induced electric dipole-type moment with unusual angular dependence, when
immersed in a quasistatic, constant external electric field. The calculation of
this effect is done in the framework of the Euler-Heisenberg effective QED
Lagrangian, corresponding to the weak field asymptotic expansion of the
effective action to one-loop order. It is argued that the neutron might be a
good candidate to probe this signal of non-linearity in QED.Comment: A misprint has been corrected, and three new references have been
adde
Vortices in U(1) Noncommutative Gauge Fields
Charged vortex solutions for noncommutative Maxwell-Higgs model in 3+1
dimensions are found. We show that the stability of these vortex solutions is
spoiled out for some, large enough, noncommutativity parameter. A non
topological charge, however, is induced by noncommutative effects.Comment: references added, slight modifications in the introduction and
conclusions. To be published in PR
Atom capture by nanotube and scaling anomaly
The existence of bound state of the polarizable neutral atom in the inverse
square potential created by the electric field of single walled charged carbon
nanotube (SWNT) is shown to be theoretically possible. The consideration of
inequivalent boundary conditions due to self-adjoint extensions lead to this
nontrivial bound state solution. It is also shown that the scaling anomaly is
responsible for the existence of bound state. Binding of the polarizable atoms
in the coupling constant interval \eta^2\in[0,1) may be responsible for the
smearing of the edge of steps in quantized conductance, which has not been
considered so far in literature.Comment: Accepted in Int.J.Theor.Phy
Finite density and temperature in hybrid bag models
We introduce the chemical potential in a system of two-flavored massless
fermions in a chiral bag by imposing boundary conditions in the Euclidean time
direction. We express the fermionic mean number in terms of a functional trace
involving the Green function of the boundary value problem, which is studied
analytically. Numerical evaluations for the fermionic number are presented.Comment: 19 pages, 4 figure
- …